1. 3 parts per billion Berlin Pond
microbial (bugs and stuff), inorganic (minerals),
pesticides (kills bugs and stuff), herbicides (kills plants)
radioactive, organic (dead stuff)
Unit
Typical Sources
old pipes,
old paint,
sinkers,
bullets,
natural mineral
deposits
ppb 3
not given
parts per billion
parts of what?
per billion what?... oh dear
Next question
Would you drink the water?

2. so, next… we need to understand the numbers
Unit
Typical Sources
old pipes,
old paint,
sinkers,
bullets,
natural mineral
deposits
ppb 3
not given
parts per billion
parts of what?
per billion what?... oh dear
define percentile….
90th percentile means that 90% of the samples tested had a level of lead
at or below 3 ppb
tells us that there were a number of measurements made
AND
that there is a range of results (not all the values are the same)
so, next… we need to understand the numbers
we need to know if they are right
and we need to know how sure we are
so how do we know which measurement is right? or if any are right?
AND how sure can we be of that conclusion?

3. the measured value is correct? (accurate)
Numbers in Science…. Accuracy, Precision (Significant Figures)
two issues with numbers….
how do we know:
if _______________________________________
and
_________________________________________
the measured value is correct? (accurate)
how certain are we of the value? (precision)
(to what place can we report our measurement?) OR
4000

5. whole numbers with respect to what we can count
Numbers in Science…. Accuracy, Precision (Significant Figures)
Types of numbers (we’ll deal with two types…)
Exact
What does ‘exact’ mean?
two types of exact numbers:
_____________________________________
ex:
whole numbers with respect to what we can count
definitions (unit equalities)
100 centimeters = 1 meter
centi means 1/100th
2.54 cm = 1 in (exactly)
1000 grams = 1 kilogram
kilo means 1000
4.184 J = 1 cal (exactly)
1,000,000,000 nanoseconds = 1 sec
nano means 1/1,000,000,000th

6. whole numbers with respect to what we can count
Numbers in Science…. Accuracy, Precision (Significant Figures)
Types of numbers (we’ll deal with two types…)
Exact
What does ‘exact’ mean?
two types of exact numbers:
_____________________________________
ex:
whole numbers with respect to what we can count
definitions (unit equalities)
100 centimeters = 1 meter
centi means 1/100th
2.54 cm = 1 in (exactly)
1000 grams = 1 kilogram
kilo means 1000
4.184 J = 1 cal (exactly)
How do we know these are correct (accurate)?
_________________________________
definitions are definitions
have to trust we counted right

7. Measured (the other type of number we’ll deal with)
start with __________________________
make a measurement…..
a single measurement
click on image for link

8. Accuracy (correctness)
Number 1 – presume that you read the instructions, and you are using the
measuring device correctly…
Next… some data:
volume
graduated cylinder _____________ Erlenmeyer flask ______________
mass
electronic (digital) balance __________ triple beam balance ____________
which do you think is right? why?
grad
cyl
Erlen
which do you think is right? why?
elec
(dig)
tbb

9. YOU DON’T WE DON’T TRUST
so,… you think “this” _____________ is more correct that “that” _______________
or,… you think “this” _______________ is more correct that “that” _______________
or,… you think “this” _______________ is more correct that “that” _______________
how do you know if either is right? _________________________________
so,…
how can these instruments be useful if you are not sure which is right
or if either is right?
Erlenmeyer
graduated cylinder
graduated cylinder
Erlenmeyer
digital balance
triple beam balance
triple beam balance
digital balance
YOU DON’T
the instruments need to have been manufactured according to some known standard
defined,
constant,
reproducible
you have to TRUST the manufacturer
for the balances, we have a ______________________
how do we know it is 200 g? _______________________
we have to _______________________
200 g standard
WE DON’T
TRUST

10. calibrate the balances…. (or any measuring device)
use a standard to check for accuracy
or adjust for accuracy
calibration marks:
the incremental marks made on an instrument
based on using a standard

11. we have to use the instrument correctly TRUST standard
Precision
How sure are we?....
The Ruler and The Red Paper (precision on single measurements)
How do we know the measured value is right? (________________)
____________________________________________
and have to _____________ the manufacturer made the instrument
according to some _______________
How certain are we of the value? (_____________)
accuracy
we have to use the instrument correctly
TRUST
standard
precision
to what place can we record our answer and with what certainty

12. THE RULER AND THE WIDTH OF THE RED PAPER
1 meter side
calibration marks ____ marks at each ____ @ _______________
know > ____ m and < ____ m
estimate > ____ m and < ____ m
somewhere between ___ ___ m to ___ ___ m 2 m
0 m and 1 m
(certain) 1
(b/c the edge of the paper
is within these “bounds” (calibration marks))
(not so certain)
(in this range)
certain
estimated
(sure / positive)
(speculated / less certain /
some guessing)
slide 14

13. (speculated / less certain /
THE RULER AND THE WIDTH OF THE RED PAPER
1 decimeter (dm) side
calibration marks ____ marks at each ____ @ _______________
know > ____ dm and < ____ dm
estimate > ____ dm and < ____ dm
somewhere between ___ ___ dm to ___ ___ dm 11 dm
0 dm, 1 dm … 10 dm
(certain) 6 7
(not so certain)
(in this range)
certain
estimated
(sure / positive)
slide 14
(speculated / less certain /
some guessing)

14. (speculated / less certain /
THE RULER AND THE WIDTH OF THE RED PAPER
1 centimeter (cm) side
calibration marks ____ marks at each ____ @ _______________
know > ____ cm and < ____ cm
estimate > ____ cm and < ____ cm
somewhere between ___ ___ cm to ___ ___ cm
101 cm
0, 1, 2, … 100 cm
(certain) 60 61
(not so certain)
(in this range)
certain
estimated
(sure / positive)
slide 14
(speculated / less certain /
some guessing)

15. the digits we are certain of…. meter side
decimeter side
centimeter side
calibrated (marked) at meters, certain of ______________
calibrated (marked) at decimeters, certain of _____________
calibrated (marked) at centimeters, certain of _______________
meters’ place
decimeters’ place
centimeters’ place
the digits we are estimating meter side
decimeter side
centimeter side
calibrated (marked) at meters, estimate ______________
calibrated (marked) at decimeters, estimate _____________
calibrated (marked) at centimeters, estimate _______________
tenth of meters’ place
tenth of dms’ place
tenth of cms’ place
the digits we are sure of correspond to ___________________________
the estimated digits correspond to _______________________________
the calibration marks
between the calibration marks

16. the estimated place depends on /determined by
the digits we are sure of correspond to ___________________________
the estimated digits correspond to _______________________________
can (and must to use the instrument correctly)
________________________________________
our rule:
we will limit our estimation on a measurement to _______ estimated place
the calibration marks
between the calibration marks
estimate between the calibration marks
1 mm (0.1 cm or m)
ONE
the estimated place depends on /determined by
the calibration marks
for the above ruler,
can (and must) estimate to the __________________________
0.1 mm (or 0.01 cm or m) place

17. dry dry dry

18. we are NOT going to do this!!
estimate
the estimated digit might be
____________ or ______________
example: _____ __ cm
a “little more”
a “little less”
certain
estimated
determines the range of possibilities
centers on the
most likely value
to know what that “little more” or “little less”
is a LOT (ideally an infinite #) of people
need to make the measurement a LOT
of times. The set of measurements would
start to center on a value and the distribution would be a normal (bell-shaped)
distribution.
we are NOT going to do this!!
The width of the distribution would be the “little more” or “little less”

19. estimate
the estimated digit might be
____________ or ______________
example: _____ __ cm
a “little more”
a “little less”
certain
estimated
determines the range of possibilities
the “littlest more” a digit can be is ______
the “littlest less” a digit can be is ______
so, for _____ __ cm, the estimated digit is in the ________________
the “littlest more” the estimated digit can be is ____
the “littlest less” the estimated digit can be is ____
+ 1
- 1
tenths place
+ .1
- .1

20. the “littlest more” a digit can be is ______
the “littlest less” a digit can be is ______
so, for _____ __ cm, the estimated digit is in the ________________
the “littlest more” the estimated digit can be is ____
the “littlest less” the estimated digit can be is ____
+ 1
- 1
tenths place
+ .1
- .1
the smallest range of possible values reflecting the uncertainty in estimating
( _______ + _____ ) cm to ( ________ - ______ ) cm OR
_________ cm to _________ cm
________ _______ cm
0.1
0.1
the range
the minimum uncertainty
on the measurement
 0.1

21. The minimum range on any measured value is _________________________
uncertainty
The minimum range on any measured value is _________________________
we (MHS Chemistry) will use this __________________________
___________________________________________
1 in the estimated digit
on single measured values
unless told otherwise
what is equally important to recognize is…
EVERY time a measurement is made,
the measured value has at least this uncertainty
so,
EVERY MEASURED VALUE HAS UNCERTAINTY
there is no such thing as an exact measurement

22. the uncertainty tells us the estimated digit
glass
80 mL 1
10 mL 1
meniscus
tens place
70 mL
80 mL 70
water
1 mL
this uncertainty
applies any time
you use the instrument
calibrated to
bottom of
meniscus
estimated
70 mL
1 mL 1
66 mL
67 mL 60
.1 mL
estimated
the uncertainty tells us the estimated digit
tells us you can, and MUST, estimate to that place

23. grams slider weight 0.1 g 1 to the best of your knowledge, the mass is-1
0.1 g 1
to the best
of your
knowledge,
the mass is
between
3.4 g
3.5 g
0.01 g
estimated
tells us you can
and MUST
estimate to that place

24. in notes, the pointer is at 5.6 (OOPS)
increments of ____ sci. not. ___  10 ___
know > ______ and < ______
estimate ________ ( ________ )
increments of ____ sci. not. ___  10 ___
know > ______ and < ______
estimate ________ ( ________ )

25. in notes, the pointer is at 5.6 (OOPS)
increments of ____ sci. not. ___  10 ___
know > ______ and < ______
estimate ________ ( ________ )
0.1 g 1 -1
this uncertainty applies
every time you use the instrument
0.01 g
increments of ____ sci. not. ___  10 ___
know > ______ and < ______
estimate ________ ( ________ )
0.1 g 1 -1
0.01 g

26. increments of ____ sci. not. ___  10 ___
know > ______ and < ______
estimate ________ ( ________ )

27. it’s right at 4!
but it’s not…
because there is no “right at 4”…

28. the width of the yellow paper…

29. The marks are called calibration marks.
Focusing on the 28 cm calibration mark.
Since the mark itself has a width,
it is not certain where 28 cm is.
One could only be absolutely certain where 28 cm is,
if the calibration mark was infinitely thin...
but then you couldn’t see the calibration mark.

30. it’s right at 4.5!
but it’s not…
because there is no “right at 4.5”…
One could only be absolutely certain
where 4.5 grams is,
if the calibration mark was infinitely thin...
and the pointer was infinitely thin…
but then
you couldn’t see the calibration mark
or the pointer.

31. because there is no “right at 4”…
One could only be absolutely certain
where 4 grams is,
if the calibration mark was infinitely thin...
but then
you couldn’t see the calibration mark.
it’s right at 4!
but it’s not…

32. increments of ____ sci. not. ___  10 ___
know > ______ and < ______
estimate ________ ( ________ )
0.1 g 1 -1
this uncertainty applies
every time you use
the instrument
0.01 g

34. dry dry dry
hang in there

35. increments of ____ sci. not. ___  10 ___
know > ______ and < ______
estimate ________ ( ________ )
50 mL 5 1
10 mL
the first place you are estimating
is the tens place
increments of ____ sci. not. ___  10 ___
know > ______ and < ______
estimate ________ ( ________ )
0.2 mL 2 -1
0.1 mL
the first place you are estimating
is the tenths place

36. increments of ____ sci. not. ___  10 ___
know > ______ and < ______
estimate ________ ( ________ )
25 mL
2.5 1
10 mL
the first place you are estimating
is the tens place

37. FINAL RULES… precision
increments of ________ sci. not. ___  10__
estimate ________ ( _______)
When the increment can be written as 1  10something
then _________________________________
_____________________________________
10 mL 1
one in the tens place 1
1 mL
uncertainty in ones place
one in the ones place
1 mL 1
graduated cylinders
.1 mL
uncertainty in tenths place
one in the tenths place
.1 g 1 -1
triple beam
balances
.01 g
uncertainty in hundredths place
one in some place
you can estimate to
one more place than the calibration (increment)

38. FINAL RULES… precision
beaker
increments of ________ sci. not. ___  10__
estimate ________ ( _______)
When the increment is NOT 1  10something
then _________________________________
_____________________________________
50 mL 5
five in the tens place 1
10 mL
uncertainty in tens place
two in the tenths place
.2 mL 2 -1
graduated
cylinder
.1 mL
uncertainty in tenths place
25 mL
2.5
two.5 in the tens place 1
Erlenmeyer
10 mL
uncertainty in tens place
NOT one in some place
you can estimate to
the same place as the calibration (increment)